High-order Iterative Methods For Computing The DMP Inverse And Core-Ep Inverse

The generalized inverse matrix has a distinctive advantage in solving the matrix equation,what's more,its applications in numerical analysis,cryptography,astronomy,economic management being recognized.Currently,the generalized inverse matrix has become an important branch of matrix theory.The Moore-Penrose inverse,Drazin inverse and Bott-Duffin inverse are important parts of the theory of generalized inverse.In 2014,the DMP inverse for a square matrix has been introduced by Malik and the Core-Ep inverse has been introduced by Prase and Mohana.It further enrichs the generalized inverse theory.Giving some appropriate conditions to compute the DMP inverse and Core-Ep inverse is a meaningful job.The main aim of this dissertation is to compute the DMP inverse and Core-Ep inverse by constructing high-order iterative methods.The dissertation is divided into four chapters:In chapter 1,we introduce the background,the present situation about the generalized inverse.We also introduce the necessary preliminaries and the main results of the text.In chapter 2,high-order iterations are given to compute DMP inverse by using the correlational properties of the DMP inverse.The necessary and sufficient conditions for the convexity of the iterative sequence and the stability analysis of the iterative sequence are also given.In chapter 3,an iterative method for computing the Core-Ep inverse is presented.We also analyse the necessary and sufficient conditions for the iterative convergence to Core-Ep inverse and give the error bounds by Frobenius norm.In chapter 4,we give a new matrix splitting-proper weak G regular splitting.We investigate its characteristics and its application to alternating iterations.